Institute for Economic Studies, Keio University

Keio-IES Discussion Paper Series

Open-access Renewable Resources and Urban Unemployment:

Dual Institutional Failures in a Small Open Economy

Ichiroh Daitoh, Nori Tarui

30 March, 2016

DP2016-009

http://ies.keio.ac.jp/en/publications/5716

Institute for Economic Studies, Keio University

2-15-45 Mita, Minato-ku, Tokyo 108-8345, Japan

ies-office@adst.keio.ac.jp 30 March, 2016

Open-access Renewable Resources and Urban Unemployment: Dual Institutional Failures in a Small Open Economy

Ichiroh Daitoh, Nori Tarui Keio-IES DP2016-009 30 March, 2016 JEL classification: O13; Q27; F18 Keywords: open access; renewable resource; urban unemployment; export tax on the resource

good; Harris-Todaro model

Abstract

This paper investigates when poverty reduction and environmental resource preservation can be compatible in developing economies with two prominent institutional failures: wage rigidity in urban labor markets and open access to rural natural resources. We develop a small open dualistic economy model with these institutional features, and investigate the effects of an export tax on the resource good on urban unemployment and overexploitation of the rural resource. At the steady state, the first-best policy calls for an urban wage subsidy while rural labor should be subsidized at a lower rate, or be taxed. A rural tax constitutes the first-best policy when the domestic price of urban manufactured good is sufficiently high. Thus the well-known first-best policy prescription by Bhagwati and Srinivasan (1974) does not apply to developing countries when the world price of the resource good is low under free trade and/or an import tariff on the manufactured good is high. Unlike what the literature indicates, an increase in the export tax rate generally reduces the rate of urban unemployment, thereby improving welfare. However, the level of urban unemployment is more likely to increase if the initial rate of export tax is lower. A small export tax always improves welfare by mitigating the two institutional failures.

Ichiroh Daitoh Faculty of Business and Commerce, Keio University 2-15-45 Mita, Minato-ku, Tokyo 108-8345, Japan idaitoh@fbc.keio.ac.jp

Nori Tarui Department of Economics, University of Hawaii at Manoa 2424 Maile Way, 518 Saunders Hall, Honolulu, HI 96822 USA nori@hawaii.edu

Acknowledgement : This work was supported by Grant-in-Aid for Scientific Research, Scientific

Research(C),No.24530241; Keio Gijuku Academic Development Funds (2013).

0

Open-access Renewable Resources and Urban Unemployment: Dual Institutional Failures in a Small Open Economy

Ichiroh Daitoh† and Nori Tarui

Keio University and University of Hawaii at Manoa

March 29, 2016

This paper investigates when poverty reduction and environmental resource preservation can be

compatible in developing economies with two prominent institutional failures: wage rigidity in

urban labor markets and open access to rural natural resources. We develop a small open

dualistic economy model with these institutional features, and investigate the effects of an

export tax on the resource good on urban unemployment and overexploitation of the rural

resource. At the steady state, the first-best policy calls for an urban wage subsidy while rural

labor should be subsidized at a lower rate, or be taxed. A rural tax constitutes the first-best

policy when the domestic price of urban manufactured good is sufficiently high. Thus the

well-known first-best policy prescription by Bhagwati and Srinivasan (1974) does not apply to

developing countries when the world price of the resource good is low under free trade and/or

an import tariff on the manufactured good is high. Unlike what the literature indicates, an

increase in the export tax rate generally reduces the rate of urban unemployment, thereby

improving welfare. However, the level of urban unemployment is more likely to increase if the

initial rate of export tax is lower. A small export tax always improves welfare by mitigating the

two institutional failures.

Keywords open-access renewable resource, urban unemployment, export tax on the

resource good, Harris-Todaro model

JEL Classification Codes：O13, Q27, F18

†Correspondence: Ichiroh Daitoh, Faculty of Business and Commerce, Keio University: 2-15-45, Minato-ku, Tokyo, 108-8345, Japan; E-mail: idaitoh@fbc.keio.ac.jp; Tel & Fax: +81-3-5418-6707. Daitoh is grateful to financial supports by JSPS KAKENHI Grant Number 24530241(Grant-in-Aid for Scientific Research(C)) and Keio Gijuku Academic Development Funds (2013).

1

1. Introduction

Development policy targets, such as the Millennium Development Goals (MDGs), often pursue

both poverty reduction and environmental preservation. The Sustainable Development Goals

(SDGs), the successor of MDGs, address the compatibility of these goals explicitly (Sachs,

2015). The economics literature has explored policies to pursue these dual development goals

based on the traditional dualistic economy model a la Harris and Todaro (1970: HT) by focusing

on relations between reduction in urban unemployment and a decrease in pollution due to urban

industrial activities (Wang, 1990; Daitoh, 2003; Beladi and Chao, 2006; Rapanos, 2007; Daitoh,

2008; Tsakiris et.al., 2008; Daitoh and Omote, 2011). These studies, with a few exceptions, have

overlooked the roles of rural environmental resources and the associated institutional issues. In

fact, imperfect institutions that govern rural natural resource use, along with an urban

institutional failure that induces persistent urban unemployment and poverty in informal sectors,

is a key challenge for many developing countries in achieving the dual SDG targets of poverty

reduction and environmental preservation.

Rural natural resources play no less important economic and environmental roles than those

of pollution from urban industries especially in poor developing economies. For example, as

Barbier (2005) finds, the majority of low- and middle-income countries are highly dependent on

primary product exports (stylized fact one on p.24) while resource dependency in those

countries is associated with poor economic performance (stylized fact two on p.32). Empirical

studies have found that such poor performance is the outcome of weak institutions governing

natural resource use (Fischer 2010, Barma et al. 2012). The compatibility between rural

resource preservation and a resolution of urban problems including unemployment has attracted

keen interests among policymakers. Izquierdo, Grau and Aide (2011) explored implications of

rural-to-urban migration for conservation of forest in Argentina. They found that under the

2

future land-use-cover scenarios they created, the rural-to-urban migration and land-use planning

could favor rural nature conservation with little impact on urban areas. This leads us to the

question of whether rural environmental preservation could be compatible with urban poverty

reduction in general given two institutional failures associated with urban labor markets and

rural natural resource use. These two failures are inter-related as the relative wage is one of the

key factors for rural-urban migration, which is another global trend across developing

economies. In particular, while discouraging rural resource exploitation (or encouraging urban

manufacturing) may mitigate resource overuse, the accompanying migration may increase urban

unemployment.

This paper attempts to answer this question by taking into account the stylized fact that rural

production depends highly on open-access renewable resources in poor developing economies.

The crucial roles of open-access renewable resources and their dynamics have already been

analyzed intensively in the trade literature. Chichilnisky (1994) found that the international

difference in property right regimes on renewable resources can be a source of gains from trade

in a two-country Ricardian trade model. Brander and Taylor (1997, 1998) showed that gains

from trade may be lost by the dynamics of open-access renewable resource stock in the long-run.

They referred to Brazil, Canada, Indonesia, Philippines and Ivory Coast as typical countries

whose export substantially depends on open-access forests. While most of them are developing

countries, none of these studies have considered a dualistic structure with urban unemployment

a la Harris and Todaro (1970), which is specific to developing economies.

Conversely, most previous studies on trade and environment based on HT models paid no

attention to the overexploitation problem concerning open-access resources. Nor did they

consider renewable resource dynamics. Dean and Gangopadhyay (1997) and Chao, Kerkvliet

and Yu (2000) considered deforestation problem in a small open dualistic economy with

3

vertically-related industries. They analyzed effects of export restriction on timber produced in

the rural sector. However, they considered the situation where competitive profit-maximizing

firms produced a rural resource good. That is, they implicitly assumed perfect property right

regime on resources, eliminating the possibility of overexploitation problem concerning

open-access resources.

We bridge the gap between these two strands of research by developing a model that captures

the two key institutional failures described above in a simple manner, i.e., a small open HT

model with an open-access resource in the rural sector. This approach provides a number of

advantages, First, this model allows us to analyze transparently when a reduction in urban

unemployment can be compatible with a decrease in overexploitation of rural resource stock. In

particular, we demonstrate how the traditional first-best policy by Bhagwati and Srinivasan

(1974) should be modified in the presence of rural open-access resources. Second, our

framework delineates the economic mechanism through which an export tax on the resource

good affects urban unemployment through a reduction in rural population (and thus an increase

in the number of the urban unemployed) and an increase in the number of urban manufacturing

workers.

The above analysis on the export tax provides important policy insights because export tax is

one of the most common policy instruments imposed on natural resource sectors in many

developing countries (WTO 2010). 1 The direction of change in urban unemployment,

influenced by the export taxes, determines whether a reduction in urban poverty will be

compatible with a decrease in overexploitation of rural resources.2 Abe and Saito (2016) is the

1 WTO (2010) notes that, while natural resources represent approximately 24 per cent of all sectors, about one-third of all export taxes recorded in WTO Trade Policy Reviews cover natural resource sectors. It also finds that export taxes occur with greater frequency in fishing and forestry (renewables) than in fuels and mining (non-renewables). 2 The rate of urban unemployment plays a critical role in evaluating social welfare in HT models. See section 5.

4

novel and only existing study, which examined the effects of an export tax on the resource good

on urban unemployment and welfare in a small open HT economy with rural environmental

resource stock. Among other results, they showed that an increase in the export tax always

raises the rate of urban unemployment but improves the environmental quality.

However, this result depends crucially on the special structure of their model. In particular,

because they choose the urban manufactured good as the numeraire, an increase in the export

tax does not affect the relative price of the urban manufactured good (because its price is always

unity) and thus the number of urban manufacturing workers is fixed in equilibrium. The higher

export tax only decreases rural production and population, which promotes migration to the city.

It necessarily increases both the number of the urban unemployed and the rate of urban

unemployment.3 In other words, the possibilities of an increase in the number of urban

manufacturing workers and of reducing the rate of urban unemployment are eliminated from the

outset in Abe and Saito (2016). Therefore, we reexamine the direction of change in the rate of

urban unemployment based on a general HT model with more price flexibility.

Our analysis generates a number of findings. First, the first-best policy given the two

institutional failures in urban and rural sectors is a combination of urban wage subsidy and a

lower rate of rural income subsidy or even a tax. This requires a modification of the traditional

first-best policy prescription by Bhagwati and Srinivasan (1974), i.e., the combination of urban

and rural wage subsidies at the same rate. In particular, a rural income tax constitutes the

first-best policy when (i) the urban fixed wage rate is lower, and/or (ii) the domestic price of the

urban manufactured good is higher (e.g., a lower world price of the resource good under free

trade and/or a higher tariff rate on the manufactured goods). Second, as opposed to Abe and

Saito (2016), a rise in the export tax rate on the resource good always reduces the rate of urban

3 In the Harris-Todaro Framework, the unemployment rate is defined as the ratio of the number of the urban unemployed to the number of urban manufacturing workers.

5

unemployment, which improves welfare. However, even so, the level of urban unemployment is

more likely to increase if the initial rate of export tax is lower (including free trade). Finally, an

increase in the export tax rate always improves welfare if this country initially engages in free

trade.

Our model captures the institutional failures related to the urban labor market and the rural

resource use in a highly stylized manner (i.e., an institutionally imposed lower bound on the

urban wage rate and open access resource use in the rural sector). Regarding the former

assumption, many studies have generalized the original HT model by endogenizing the wage

rigidity in the urban labor market (de Janvry and Sadoulet 2016, p.443; Todaro and Smith

2015, pp.361-362) and by modeling the urban informal sector formally (e.g., Gupta 1993).

While generalizing our model in these directions will not change our main results about the

nature of the first-best policy and the impacts of export taxes, extending the model further

beyond may generate richer results. We will discuss the policy implications of our results, along

with the opportunities for extending our analysis, in the last section of the paper.

2. The Model

Consider a small open two-sector Harris-Todaro (1970) economy exporting a resource good,

which is produced in the rural sector, and importing a manufactured good, which is produced in

the urban sector. While the resource good is assumed to be the numeraire, the price 0 of

the urban manufactured good is given in the world market. Under free trade, its domestic price

is equal to . As the simplest way to introduce an institutional failure of the urban labor

market, we assume that the urban wage rate is institutionally fixed at a level 0 that

exceeds any prevailing market clearing level, so that urban unemployment exists in equilibrium.

Let 0 be the output level (harvest) of the resource good, which is produced with

6

0 units of rural labor and a renewable resource stock 0. We assume the Schaefer

production function:

(1) ,

where α 0 represents the efficiency of resource good production. To represent an

institutional failure with respect to the natural resource management, we assume that the

resource is subject to open access. Thus agents in the rural sector can freely use the service of

to produce . With this assumption, the opportunity cost of labor 0 and the rural labor

input satisfy the zero-rent condition in equilibrium:4

(2) .

The renewable resource stock evolves over time depending on the natural growth of the

resource and the harvest. We assume a logistic growth function of the renewable resource

1 where 0 is the intrinsic growth rate of the resource and 0 the

carrying capacity. At any point in time t, the resource stock will grow according to

. We focus on the steady state where 0:

(3) 1 .

Equalities (1) and (3) imply the following relationship between the steady-state stock level and

the associated labor input:

(4) 1

The associated sustainable yield satisfies .

The urban manufacturing output 0 and the labor input (i.e., the urban employment)

0 satisfy where is the production function with 0and " 0.

The representative firm of competitive urban manufacturing sector maximizes its profit,

4 We should interpret not as a wage rate but as an income per capita in the rural sector because rural agents produce the resource good using their own labor.

7

employing labor up to the level where the value marginal product of urban manufacturing

labor (MPLM) in terms of domestic price equals the institutionally fixed wage rate:

(5) .

As in the standard HT model, the equilibrium allocation of labor between the rural and the

urban sectors induces the equalization of expected wage/income between rural and urban areas:

(6) ,

where ≡ / is the urban unemployment rate, and the level of urban unemployment.

The total population 0 in the economy is fixed and consists of rural labor, urban

manufacturing employment, and urban unemployment:

(7) 1 .

The general equilibrium system of (1), (2), (3), (5), (6) and (7) determines the values of six

endogenous variables , , , , , . It can be solved as follows. First, substituting (4) into

(2), we have:

(8) 1 .

To ensure that the model has a unique interior solution for the open-access general equilibrium

and for the efficient resource allocation problem in the next section, we assume:

Assumption 1: 2 holds.

Under this condition, the opportunity cost of rural labor is always positive in equilibrium.

Next, we have from (6) and (8):

(9) 1 1 .

The combinations of ( , 1 ) satisfying (9) are represented by the increasing convex curve

8

Rr in Figure 1. The intercept on the vertical axis is / . Finally, given ∗ determined

by (5), the combinations of ( ,1 ) satisfying (7) are represented by the decreasing line

in Figure 1. The intercept on the vertical axis is / ∗ . If lies above , there exists

a unique equilibrium in our model. Then, we obtain the next proposition.

Proposition 1. Under Assumption 1, there is a unique interior equilibrium that satisfies

(10) ∗ .

Figure 1. Existence and Uniqueness of Equilibrium

3．First-best Policy

We now investigate the first-best policy for this economy with two kinds of distortions; open

access to the rural resource and urban wage rigidity. This policy could also be interpreted as

providing a theoretical prescription that makes poverty reduction and environmental resource

preservation compatible in a dualistic developing economy.

On one hand, taxing the rural production may be justified because open access leads to

resource overexploitation. On the other hand, a reduction in urban unemployment requires a

r

H 1+μ＊

LR O

R

L

M

1+μ

LR＊

9

rural subsidy that will expand rural population to hinder excessive rural-to-urban migration.

Bhagwati and Srinivasan (1974) showed in the standard HT model (without rural open-access

resources) that the first-best policy is the combination of rural and urban wage subsidies at the

same rate. This section shows that the first-best labor allocation is attained in our model by a

combination of the urban wage subsidy and a lower rate of rural income subsidy, or even a tax.5

Then we investigate when the first-best policy combination consists of a rural income tax.

3.1 First-best Labor Allocation and Urban Wage Subsidy

Let us first define the first-best labor allocation. It is attained when the value marginal products

of labor are equalized across the rural and the urban sectors.6 While the value is

′ , the value of (sustainable) marginal product of rural labor ( ) is given by

1 . With the full-employment condition , the efficient

labor allocation , is characterized by

(11) ′ 1 .

This is shown by point in Figure 2. Because the right-hand side of (11) is positive by

Assumption 1, an interior solution E exists if the value is lower than when

, 0, , i.e., if ′ holds.

5 We assume that the subsidies are financed by a lump-sum tax levied on consumers and that tax revenues net of subsidies are distributed in a lump-sum fashion among consumers. 6 This efficient labor allocation in our “sustainable yield” model corresponds to the solution to the associated dynamic optimization problem with the discount rate close to zero. See Appendix A.

10

Figure 2. Rural Income Subsidy

If the government provides each urban firm with the wage subsidy , the mass

of workers are employed in the urban manufacturing sector. Because the urban wage rate

received by the workers will be equal to the fixed urban wage rate , each manufacturing

worker has no incentive for migration. This urban wage subsidy will thus support the efficient

labor allocation .

3.2 Rural Subsidy

In order to derive the first-best policy in the rural sector, we introduce the line representing

the (sustainable) average product of rural labor (8) in Figure.2. If the government provides each

rural producer with the subsidy , rural income per capita received will be equal to

the fixed urban wage rate . Then each rural worker has no incentive to migrate to the urban

area, and thus the number of people will work in the rural resource sector. Therefore, the

first-best policy is the combination of the urban wage subsidy and the rural income

subsidy .

3.3 Should Rural Resource Use be Taxed?

When the domestic price of the manufactured good is relatively high, the first-best policy in

the rural sector will not be a subsidy but a tax on rural income per capita. Figure 3 describes this

KG

F

w M Mw s

Mw

( )RR L ERL

E

OROM

'( )MpF L

11

case: if the government imposes a tax on each rural producer, the disposable income

of a rural producer is represented by the height of point G, which is equal to . Then he/she

has no incentive for rural-urban migration.

Figure 3. Rural Income Tax

Let us now investigate when the rural first-best policy is a tax. Consider the benchmark case

where the line for average product of rural labor (8) passes through point G. Then the

government should set the rural income subsidy at zero ( 0). If at holds, the

rural income tax combined with the urban wage subsidy gives rise to the first-best

labor allocation . From the inequality above, we obtain the necessary and sufficient condition

for rural income tax:

(12) 1

When is (12) likely to hold? Using Figure 2 or 3, we can examine how the efficient labor

allocation is affected by exogenous parameters. First, (12) is more likely to hold when (a) the

urban fixed wage rate is lower and (b) is higher. Second, the effects of the other

parameters are, in general, ambiguous (see Appendix B). Thus we obtain the next position.

Proposition 2:

(i)The first-best labor allocation is attained by a combination of the urban wage subsidy

K

G

F

w M Mw s

Mw

( )RR L

ERL

E

OROM

'( )MpF L

12

and a lower rate of rural income subsidy , or even a tax .

(ii)The rural income tax combined with the urban wage subsidy gives rise to the

first-best labor allocation if and only if (12) holds. Thus the first-best rural policy is more

likely to be a tax when (a) urban fixed wage rate ( ) is lower, and/or (b) the domestic price

of urban manufactured good ( ) is higher. The relations of K, r and are, in general,

ambiguous.

The reason for result (ii)-(a) to hold is that is given independently of the other parameters

when determining the first-best labor allocation. The reason for (ii)-(b) is as follows. When p is

higher, the ′ curve lies at a higher position. The value of (the length of in

the figure) is smaller and thus the first-best labor allocation corresponds to a lower level of rural

population . Because of the diminishing returns to rural labor, the (sustainable) rural

income per capita tends to be higher than the fixed urban wage. This requires a tax that

reduces disposable income of rural people so that they have no incentive for rural-to-urban

migration.

Result (ii)-(b) has two important economic implications. First, under free trade, the first-best

policy combination is more likely to be a rural income tax with urban wage subsidy when the

world price of the urban manufactured good is higher, or, equivalently, when the world price

1/ of the resource good is lower. In this situation the traditional first-best policy proposed by

Bhagwati and Srinivasan (1974), i.e., the combination of urban and rural wage subsidies at the

same rate, will not apply to modern dualistic developing economies whose production highly

depend on rural open-access resources.

Second, the first-best rural policy will be a rural income tax, not subsidy, when this country

imposes a high import tariff on the urban manufactured good (which increases the domestic

13

price p). This situation seems realistically relevant to low- and middle-income developing

countries. By Lerner’s symmetry theorem, when the government sets a high export tax on the

rural good for preservation of environmental resource stock such as forests (see section 4 in

further details), the first-best policy will be a rural income tax with urban wage subsidy. In this

situation, rural residents suffer from both the export tax and the rural income tax. Domestic

income inequality between rural and urban areas will be aggravated.

4．Export Tax on the Resource Good

We will now investigate the effects of a rise in the export tax rate on the resource good to

compare our results with those in Abe and Saito (2016). We show that, at the steady state,

preservation of rural renewable resource stock is consistent with a reduction in urban

unemployment.

4.1 Open-access Equilibrium with Export Tax

Let 0 be the ad-valorem tax rate on the export of the resource good.7 The world relative

price of the resource good is higher than its domestic price, i.e., 1 ⁄ 1 1 .⁄ Then the

domestic price of the urban manufactured good is 1 , with its world price given

exogenously. Recall that the open-access equilibrium is given by (5), (7) and (9). The

equilibrium urban manufacturing employment will then be ∗

, where is the

inverse function of ′ and ′ 0 holds. The line will be 1 ∗ with the

vertical intercept ∗ .

7 In section 2 we have used t as a time variable. We focus here on the steady state and use t to represent an export tax.

14

Figure 4. Effect of an Increase in the Export Tax

4.2 The Effect on the Rate of Urban Unemployment

Let us first investigate the effect of a rise in on the rate ∗ of urban unemployment, which

influences the equilibrium welfare in a critical manner. When is raised, the urban

manufacturing employment ∗ increases and thus the line shifts downward to ′

in Figure 4. Because the curve remains unchanged, the equilibrium moves from to ′.

Therefore the rural population ∗ decreases while the rate ∗ of urban unemployment

decreases. The rural income ∗ / 1 ∗ increases.

Proposition 3: A rise in the export tax rate on the resource good always

(i) reduces the rate ∗of urban unemployment, (ii) decreases rural population ∗ , and (iii)

increases the rural income per capita ∗.

Result (i) is opposite to what Abe and Saito (2016) find (that a rise in the export tax rate

increases the rate of urban unemployment) due to the following reason. Because Abe and Saito

(2016) choose the urban manufactured good as the numeraire, a rise in the export tax rate on the

resource good does not affect the relative price of the urban manufactured good (whose price is

*1 '

*1

* 'RL *RL

H’

'M

r

H

LR O

R

L

M

1+μ

15

always unity) in their model. 8 Thus the urban manufacturing employment ∗ remains

unchanged. On the other hand, a rise in the export tax rate decreases the rural production and

population, promoting the rural-to-urban migration, thereby increasing the urban population

∗ ∗ . With ∗ fixed, both the level ∗ and the rate ∗ ∗ / ∗ of urban

unemployment increase in their model. In contrast, our model captures a change in ∗ due to

the trade policy change because we choose the resource good as the numeraire. Then a rise in

the relative price of the manufactured good expands the urban manufacturing employment

and thus decreases rural population. Because of the decreasing returns to rural labor, the rural

income per capita rises and thus the rate of urban unemployment declines (see equation 6).

Therefore, a rise in the export tax on the resource good will not increase but reduce the rate of

urban unemployment. 9 In this sense, a reduction in urban unemployment will be compatible

with the preservation of rural resource stock.10

However, the level of urban unemployment may or may not decrease as demonstrated below.

If it increases, a higher export tax rate on the rural resource good could be interpreted as

aggravating the urban poverty.

4.3 The Effect on the Level of Urban Unemployment

Here we derive a necessary and sufficient condition for the level of urban unemployment, ∗ ,

to be increasing in the export tax rate. It follows from (6), (7), and (8) that the equilibrium

satisfies α 1 ∗ . Total differentiation yields

8 Other differences include (i) the number of resource users is exogenous and independent of urban-rural migration in Abe and Saito (2016) while it is endogenous and directly linked to migration in our model; and (ii) the resource dynamics is not taken into account in Abe and Saito’s framework. 9 Appendix C shows that if we chose the manufactured good as the numeraire without changing the other parts of the model, the urban unemployment rate would be increasing in the export tax rate. 10 The rural-urban income gap shrinks by result (iii). The export tax tends to correct income inequality as well.

16

1 . Thus we obtain

(14) ∗

∗ 0.

It follows from ｄ 0 that the necessary and sufficient condition for

∗

∗ 0 is ∗

∗ 1. Using (14), it is equivalent to

(15) 1 .

To find what kind of equilibrium we should focus, from (8), (15) is rewritten as:

(16) ∗ ∗ / .

This inequality implies that a rise in the export tax rate on the resource good increases the level

of urban unemployment when the production of this economy depends highly on the resource

good sector ( ∗ is large) and the rural-urban income gap ( ∗) is large.

When is (15) or (16) likely to hold? Although the effects of exogenous parameters , , ,

and on the right-hand side are ambiguous (see Appendix D), we can find unambiguous

effects of the domestic price of the urban manufactured good. When the initial value of is

lower, ∗ is smaller and thus, in Figure 4, the line lies at a higher position. Then ∗

is larger and ∗ is lower. Therefore, (16) is more likely to hold when the initial domestic price

is lower. In light of Lerner’s symmetry theorem, we obtain:

Proposition 4: A rise in the export tax rate on the resource good increases the level of urban

unemployment if and only if this country’s domestic price of the urban manufactured good is

sufficiently low. This situation occurs when (i) the world price of the manufactured good is low

under free trade, (ii) an initial rate of export tax on the resource good is low, and/or (iii) an

initial rate of import tariff on the manufactured good is low.

17

Let us make an intuitive explanation for this proposition. When the domestic price is low, this

economy tends to have large population ∗ in the rural resource good sector at the initial

equilibrium. Then, a rise in , which leads to a higher value of , expands the urban

manufacturing sector and induces rural-to-urban migration. The urban population will increase

until the rural income per capita is equalized to the urban expected wage / 1 μ . The

size of the migration depends on the elasticity of rural labor demand. Totally differentiating (8),

we have , and thus . Using (8), the elasticity of rural labor

demand is:

(17) ε 1 1,

which is positive by Assumption 1. Because the rural population ∗ is large at the initial

equilibrium, the elasticity of rural labor demand will be small. Thus rises more slowly

when rural people migrate to the urban sector. However, because the rural population is large,

the absolute number of migrants will be large.

On the other hand, when is low, a rise in (the size of the increment ) corresponding

to the same rate of increase in gross export tax rate 1 will be small (because of

derived from ). Thus the upward shift of the value MPLM curve will be small.

Then an increase in the urban manufacturing employment will be small while the number of

migrants from the rural sector will be large. Therefore, the number of people unemployed in the

city will increase. This tends to increase the level of urban unemployment.

Furthermore, we can obtain economic implications from these results. Result (i) implies that

when this country initially engages in free trade and the world price (1/ ) of the exported

resource good is high, a rise in the export tax rate tends to increase the level of urban

unemployment. Thus restricting the export of resource intensive goods may make reducing

18

urban unemployment and preserving rural resources incompatible.

Results (ii) and (iii) imply that an introduction of the export tax on the resource good will

decrease the level of urban unemployment if this country initially sets a high import tariff rate

on the urban manufacturing good. We observe such policy mix with many resource-rich

developing economies. Thus preserving natural resources is compatible with a reduction in

urban unemployment in these cases. However, if the tariff is reduced in the worldwide trade

liberalization, these two goals may come to be incompatible.

5. Welfare Consideration

In this section we investigate whether a rise in the export tax rate on the resource good improves

welfare of the entire economy. Suppose that each consumer’s utility function is homothetic in

the consumption of the resource good and the manufactured good . Let 1, ,

represent the representative consumer’s (minimum) expenditure given the domestic price

1 and utility level . The aggregate consumption expenditure is equal to the

aggregate revenue in terms of the domestic price, i.e., , where

is the tax revenue measured in the resource good. In terms of the world price,

holds, as usual. Given , the value of export equals that of import,

, where ≡ is the compensated demand for the manufactured

good. Thus the export tax revenue , which is redistributed to consumers in a

lump-sum fashion, can be written as . Therefore the representative consumer’s

budget constraint in terms of the domestic price is:

(18) 1, , ＝ .

Totally differentiating (18) and rearranging the terms (see Appendix E), we obtain:

19

(19) ,

where ≡

0 and ≡

0 are the own-price elasticities of the

compensated demand for and the supply of the manufactured good. A rise in has two welfare

effects. The first term on the right-hand side of (19) represents a positive effect due to a decrease

in urban unemployment rate ( ⁄ 0) while the second term a negative effect due to the

decrease in the import of the manufactured good, i.e., in the export of the resource good. The

latter holds because small values of and/or imply that the domestic demand for the

manufactured good decreases and/or its supply increases to a small extent.11 The welfare will

improve if the effect of the reduction in urban unemployment rate is sufficiently large and/or

when the country’s trade volume decreases to a sufficiently small extent. Furthermore, if this

country initially engages in free trade ( 0 ), the welfare necessarily improves by an

introduction of the export tax on the resource good.

Proposition 5: Taxing the export of the resource good improves welfare when it decreases the

country’s trade volume to a sufficiently small extent. Furthermore, starting from free trade, a

marginal increase in the export tax necessarily improves the welfare.

Now we summarize the policy implications regarding the compatibility between urban poverty

reduction and rural resource preservation in a small open dualistic economy. Let us focus on the

realistically relevant situation where a developing country, which is highly dependent on rural

renewable resources, sets a high import tariff rate on the urban manufactured good. First, from

Proposition 2, the first-best policy consists of a rural income tax combined with an urban

11 See Appendix E for an explicit expression relating the second term on the right-hand side of (19) to the corresponding change in trade volume.

20

wage subsidy , because the domestic price of the urban manufactured good is high. This

is in a sharp contrast to the traditional policy prescription by Bhagwati and Srinivasan (1974)

that the first-best policy is the combination of the urban and rural wage subsidies at the same

rate. Second, a rise in the export tax rate on the resource good will decrease not only the rate

(Proposition 3) but also the level of urban unemployment (Proposition 4), thereby improving

welfare (Proposition 5).

Hence, the developing country under consideration tends to have an incentive to restrict

resource-good exports, which can contribute to preservation of resource stock. Conversely,

suppose that a developing country sets low tariffs on the urban manufactured goods initially.

Then it will likely experience an increase in the level of urban unemployment when an export

tax on the resource good is introduced. Under such circumstances, urban poverty reduction and

rural resource preservation will not be compatible.

6. Concluding Remarks

This paper explores when poverty reduction and resource preservation can be compatible in

modern developing economies whose production highly depends on open-access renewable

resources. By applying a small open dualistic economy model with urban unemployment and a

rural open-access renewable resource, we characterize the first-best policy combination. We also

investigate whether reducing urban unemployment is compatible with a decrease in the

overexploitation of rural resources when an export tax rate on the resource good rises. At the

steady state, the first-best policy consists of a combination of urban wage subsidy and a lower

rate of rural income subsidy or even a tax. This requires a modification of the well-known

first-best policy combination by Bhagwati and Srinivasan (1974). In particular, the first-best

policy is more likely to include rural income tax when (i) the urban fixed wage rate is lower

21

and/or (ii) the domestic price of urban manufactured good is higher (e.g., a lower world price of

the resource good under free trade and/or a higher import tariff on the manufactured good). In

contrast to Abe and Saito (2016), a rise in the export tax rate generally reduces the rate of urban

unemployment, which improves welfare. However, the level of urban unemployment is more

likely to increase if the initial rate of export tax is lower. Finally, a rise in the export tax rate

always improves welfare if this country initially engages in free trade.

Our analysis could be extended in several directions. First, we assume that harvesting from a

renewable resource is the only production activity in the rural sector. This assumption rules out

other activities such as agriculture in the rural sector. On one hand, labor reallocation from

direct resource use to agriculture may alleviate resource overuse. On the other hand, agriculture

might accelerate resource overuse in some cases (e.g., land conversion for agriculture that

contributes to deforestation).12 Taking into account such multiple rural activities may result in

richer findings on rural-urban migration, resource use, and poverty reduction. Second, we

assume that labor is the only primary factor of production (except for the resource stock) and

rule out endogenous investment in (physical) capital. Third, our analysis does not consider

environmental externalities associated with the rural resources. Finally, we concentrated on the

steady state of the renewable resource stock. Further studies could investigate the properties of

equilibrium and welfare along non-stationary transition paths.

12 Jinji (2006) studies how international trade influences deforestation when the resource’s carrying capacity is endogenous.

22

Appendix A: Sustainable Yield and Dynamically Efficient Outcome

In section 2 we derived the first-best labor allocation using (5) and :

(11) 1 .

This corresponds to the first order condition for the problem of deriving the efficient sustainable

yield that maximizes the rent . Solving (11), we have:

1 .

The above efficient outcome for the “sustainable yield” model is the (dynamically) efficient

outcome, i.e., the solution to the associated dynamic optimization that maximizes the present

value of rents over time if the discount rate is (close to) zero. To see this, consider the following

dynamic optimization problem:

max ∞

. . 1 / 0,

given where 0 is the discount rate. (Here we let ≡ .) Let be the associated

current-value Hamiltonian:

1 / .

The condition for optimality is given by

0

(at the singular solution) and the following adjoint equations:

.

At the steady state, we have 0 and harvest equal to natural resource growth:

1 / . (The time subscript is omitted here.) It then follows form the adjoint equation

that

23

/ .

As → 0 we have

, . . , .

Plug this into the first order condition (for the singular solution) and we have

0.

Because harvest equals natural resource growth at the steady state, we have 1 / ,

i.e., . Substitute this into the last expression and we have

1 .

Therefore,

1 .

This is the same as the efficient outcome for the sustainable yield model derived from (11).

Appendix B: Effects of Parameters on the Efficient Labor Allocation

This appendix shows that the effects of changes in K, r and on are, in general,

ambiguous. Totally differentiating (11), we get:

"

= α 1 α ′ 1 .

Under Assumption 1, we have 1 0, the relations of exogenous parameters to the

efficient labor allocation are:

0, 0, 0.

However, 0 holds if and only if 1 0 is satisfied. Therefore, as shown in the

24

text, the first-best rural policy is more likely to be a tax when the domestic price of urban

manufactured good (p) is higher.

However, an increase in and in raises the value of , but does not always raises the

right-hand side of (12). An increase in α has an ambiguous effect on the value of and thus

on the right-hand side of (12). Therefore the relations of , r and are, in general, ambiguous.

Appendix C: The Model with Manufactured Good as the Numeraire

This appendix shows that the urban unemployment rate would increase by a rise in the export

tax rate as in Abe and Saito (2016) if we chose the manufactured good as the numeraire. As

demonstrated below, the choice of the numeraire plays a crucial role in determining the

direction of change in ∗.

Let us denote the domestic relative price of the resource good as q. In this revised model,

given , , , the system of the six equations determines the same six unknowns as in the

text. Note that is fixed in terms of the manufactured good.

, (1)

, (2’)

1 , (3)

′ , (5’)

, (6)

1 . (7)

Let us explain how to solve it. First, ∗ is pre-determined by (5’). Then the ML line

(7) 1 ∗ remains unchanged. Consider how the Rr curve is revised.

1

*(1 )

*(1 ) '

*RL

* 'RLLR

M

L

R

R’

r r’

25

Substituting (1) into (3) yields (5) S 1 in the text. Substituting this into (2’)

and eliminating by using (6), we get the revised Rr curve:

(11’) 1 1 .

Observe that the slope of the revised Rr curve, /

/, does not directly depend on

q.

A higher export tax rate implies a lower domestic price of resource good . Then the revised

Rr curve shifts upward. However, the ML line remains unchanged because ∗ does not change

in this model (see equation 5’). Thus, ∗ decreases while 1 ∗ increases in equilibrium.

The rate ∗ of urban unemployment would increase in our model if we chose the

manufactured good as the numeraire as in Abe and Saito (2016). For the reason explained in the

main text, we argue that the resource good should be taken as the numeraire.

Appendix D: Effects of Parameters on Open-access Equilibrium ∗

First, total differentiation of 1 ∗ in section 4.3 yields

1

1 1 12

∗ ∗ .

Rearranging the terms, we obtain:

1

1 1 12

∗ ∗ .

26

Under Assumption 1, 1 ∗ 0 holds. Then we have:

∗

0,∗

0,∗

0,∗

0,∗

∗ 0.

The effect of a change in on ∗ is ambiguous because a rise in directly decreases

∗ but increases it through a reduction in ∗ .

Appendix E: Derivation of Welfare Formula (19)

Total differentiation of (18) yields;

.

Using , ′ and from the zero-rent

condition , we get ;

′

.

′ .

Remembering (6) and (7), we have and 1 .

Substituting them, we get;

1 ′ .

Using (5) and (7), and rearranging the terms, we obtain

.

The second terms on the right-hand side satisfies

,

Thus we obtain (19) in the text.

27

References

Abe, Kenzo, and Muneyuki Saito, 2016. “Environmental Protection in the Presence of

Unemployment and Common Resources”, Review of Development Economics, Vol.20, No.

1, pp. 176–188.

Barbier, Edward, 2005. Natural Resources and Economic Development, Cambridge University

Press.

Barma, Naazneen H.; Kaiser, Kai; Le, Tuan Minh; Vinuela, Lorena. 2012. Rents to Riches? The

Political Economy of Natural Resource-led Development. World Bank.

Beladi, Hamid and Chi-Chur Chao, 2006. “Environmental Policy, Comparative Advantage, and

Welfare for a Developing Country,” Environment and Development Economics 11,

pp.559-68.

Bhagwati, Jagdish N and T N, Srinivasan, 1974. "On Reanalyzing the Harris-Todaro Model:

Policy Rankings in the Case of Sector-Specific Sticky Wages," American Economic

Review Vol.64, No.3, pp.502-08.

Brander, James A. and M. Scott Taylor, 1997. “International Trade and Open-Access Renewable

Resources: The Small Open Economy Case,” Canadian Journal of Economics Vol.30,

No.3, pp.526-552.

Brander, James A. and M. Scott Taylor, 1998. “Open Access Renewable Resources: Trade and

Trade Policy in a Two-country Model”, Journal of International Economics 44,

pp.181-209.

Chao, Chi-Chur, Joe R. Kerkvliet, and Eden S. H. Yu, 2000. “Environmental Preservation,

Sectoral Unemployment, and Trade in Resources”, Review of Development Economics,

4(1), pp.39-50.

Chichilnisky, Graciela, 1994. “North-South Trade and the Global Environment”, American

Economic Review Vol.84, No.4, pp.851-874.

Daitoh, Ichiroh, 2003. ”Environmental Protection and Urban Unemployment: Environmental

Policy Reform in a Polluted Dualistic Economy”, Review of Development Economics Vol.7,

No.3, pp.496-509.

Daitoh, Ichiroh, 2008. ”Environmental Protection and Trade Liberalization in a Small Open

Dual Economy”, Review of Development Economics 12(4), pp.728-736.

Daitoh, Ichiroh and Masaya Omote, 2011. ”The Optimal Environmental Tax and Urban

Unemployment in an Open Economy”, Review of Development Economics 15(1), pp.

28

168-179.

de Janvry, Alain and Elisabeth Sadoulet, 2016. Development Economics: Theory and Practice.

Routledge.

Dean, Judith M. and Shubhashis Gangopadhyay, 1997. “Export Bans, Environmental Protection,

and Unemployment”. Review of Development Economics 1(3), pp.324-336.

Gupta, Manash Ranjan, 1993. “Rural-urban migation, informal sector and development policies:

A theoretical analysis”. Journal of Development Economics 41, pp.137-151.

Fischer, C., 2010. “Does trade help or hinder the conservation of natural resources?”. Review of

Environmental Economics and Policy, 4 (1), pp.103-121.

Harris, John R. and Michael P. Todaro, 1970. “Migration, Unemployment and Development: A

Two-Sector Analysis,” American Economic Review Vol.60, pp. 126-42.

Izquierdo, Andrea E, He´ctor R. Grau and T. Mitchell Aide, 2011. ”Implications of Rural–Urban

Migration for Conservation of the Atlantic Forest and Urban Growth in Misiones,

Argentina (1970–2030),” AMBIO 40, pp.298-309.

Jinji, Naoto, 2006. “International Trade and Terrestrial Open-Access Renewable Resources in a

Small Open Economy”, Canadian Journal of Economics Vol. 39, No. 3, pp.790-808.

Rapanos, Vassilis T., 2007. “Environmental Taxation in a Dualistic Economy,” Environment and

Development Economics 12, pp.73-89.

Sachs, Jeffrey, D., 2015. The Age of Sustainable Development, Columbia University Press, New

York.

Todaro, Michael P. and Stephen C. Smith, 2015. Economic Development, 12th edition. Pearson

Education Limited.

Tsakiris, Nikos, Panos Hatzipanayotou, and Michael S. Michael, 2008. “Pollution, Capital

Mobility and Tax Policies with Unemployment,” Review of Development Economics 12,

pp.223-36.

Wang, Leonard, 1990. “Unemployment and the Backward Incidence of Pollution Control,”

Journal of Environmental Economics and Management 18, pp.292-98.

World Trade Organization, 2010. World Trade Report 2010: Trade in natural resources.